Estimation of Variance Components : What is Missing the EM Algorithm ?

The EM algorithm is a frequently advocated algorithm for the estimation of variance components. A faster converging algorithm is developed using alternative parameter-izations based on the analysis of variance. The procedure is exemplified using designs with two and three variance components and wi.th multivariate designs using parameter values relevant to animal breeding data. 1. THE MODEL We consider estimation in linear models specified by y=X~+ ~ Z~bi+e (1.1) where y is a n × 1 vector of observed responses, X and Zi (i = 1 ..... c) are known matrices of size n×p and n ×qi, ~ is a p× 1 vector of fixed effects, and each b~ is a q~×l vector of random effects distributed independently as N(0, ~r~ZI) and e is a n × 1 vector of error 215